A229441 Number of n X 4 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

6, 14, 37, 109, 324, 915, 2402, 5843, 13229, 28071, 56234, 107080, 194989, 341334, 576993, 945488, 1506848, 2342300, 3559899, 5301215, 7749202, 11137381, 15760476, 21986649, 30271487, 41173901, 55374104, 73693842, 97119059, 126825184

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (1/5760)*n^8 + (1/2016)*n^7 + (1/576)*n^6 + (11/360)*n^5 + (409/5760)*n^4 + (49/288)*n^3 + (41/96)*n^2 + (2771/840)*n + 2.

Conjectures from Colin Barker, Sep 17 2018: (Start)

G.f.: x*(6 - 40*x + 127*x^2 - 224*x^3 + 255*x^4 - 177*x^5 + 77*x^6 - 19*x^7 + 2*x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)

Example

Some solutions for n=4:
..0..2..2..2....0..0..0..0....0..2..2..2....0..0..2..2....0..0..0..0
..1..0..0..0....1..1..1..1....1..0..2..2....0..0..2..2....1..1..1..1
..1..0..0..0....1..1..1..1....2..1..0..2....1..1..0..0....2..2..2..2
..1..1..1..1....2..2..2..2....2..2..1..0....2..2..1..1....2..2..2..2

Crossrefs

Column 4 of A229445.

Sequence in context: A272548 A036387 A053560 * A119874 A344380 A270127

Adjacent sequences: A229438 A229439 A229440 * A229442 A229443 A229444

Keyword

nonn

Author

R. H. Hardin, Sep 23 2013

Status

approved